The table shows the amount of milk that Wisconsin dairy farms produced from 1940 to 1997. Use a linear model to estimate milk production in 1990.
Year
Milk Produced
(in billions of lbs.)
1940
7
1972
7
1997
8
(1 point)
Responses
15.1
15.1
12.5
12.5
7.5
7.5
2.5
To estimate milk production in 1990 using a linear model, we can use the values from the two given years to find the equation of the line. We can then substitute the year 1990 into the equation to get our estimate.
First, we need to find the slope of the line. The slope can be found by calculating the change in milk production divided by the change in years.
Slope = (8 - 7) / (1997 - 1972) = 1 / 25 = 0.04
Now, we can use the slope and one of the given points (1940, 7) to find the equation of the line using the point-slope form: y - y1 = m(x - x1).
Using the point (1940, 7):
y - 7 = 0.04(x - 1940)
Simplifying the equation:
y - 7 = 0.04x - 77.6
y = 0.04x - 70.6
Now, we can substitute the year 1990 (x = 1990) into the equation to find the estimated milk production in 1990:
y = 0.04(1990) - 70.6
y = 79.6 - 70.6
y = 9
Therefore, the estimated milk production in 1990 using the linear model is 9 billion lbs.